US7324601B2 - Coarse frequency synchronization method and apparatus in OFDM system - Google Patents
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L7/00—Arrangements for synchronising receiver with transmitter
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2647—Arrangements specific to the receiver only
- H04L27/2655—Synchronisation arrangements
- H04L27/2668—Details of algorithms
- H04L27/2673—Details of algorithms characterised by synchronisation parameters
- H04L27/2675—Pilot or known symbols
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/26—Systems using multi-frequency codes
- H04L27/2601—Multicarrier modulation systems
- H04L27/2647—Arrangements specific to the receiver only
- H04L27/2655—Synchronisation arrangements
- H04L27/2657—Carrier synchronisation
- H04L27/2659—Coarse or integer frequency offset determination and synchronisation
Definitions
- the present invention relates to a coarse frequency synchronization method and apparatus for an orthogonal frequency division multiplexing (OFDM)—based system, and more particularly, to a coarse frequency synchronization method and apparatus in an OFDM receiver.
- OFDM orthogonal frequency division multiplexing
- FIG. 1 is a block diagram showing the structure of a conventional OFDM receiver system.
- the conventional OFDM receiver system includes an OFDM demodulator 10 and a frequency synchronizer 12 .
- the OFDM demodulator 10 includes a RF receiver 101 , an analog-to-digital converter 102 , an I/Q filter 103 , a frequency corrector 104 , an FFT unit 105 , and a Viterbi decoder 106 .
- the frequency synchronizer 12 includes a buffer register 121 , a complex data multiplier 122 , an IFFT unit 123 , a maximum value detector 124 , a counter 125 , and a reference symbol generator 126 .
- the analog-to-digital converter 102 quantizes the received RF signal.
- the I/Q filter 103 then separates In-phase and Quadrature (I/Q) component signals from the quantized signal.
- the frequency corrector 104 corrects a frequency error of the filtered signal, and the FFT unit 105 receives the frequency corrected signal and performs a Fast Fourier Transform in order to demodulate the signal.
- a Viterbi decoder 106 decodes the demodulated signal.
- the demodulated signal is stored in the buffer register 121 of the frequency synchronizer 12 and output as a reception signal X.
- the complex data multiplier 122 multiplies the complex conjugate of Zk by Xk, an inverse FFT (IFFT), denoted by h n , is performed on the result of the multiplication, as shown in Equation 1 below, and then the result of the IFFT is output.
- IFFT inverse FFT
- Equation (1) Equation (1) can be rewritten as Equation (2):
- Equation (2) is obtained using the process for calculating convolutions of two signals in the time domain, and the resulting value h n is a channel impulse response (CIR).
- CIR channel impulse response
- the OFDM receiver system that recognizes a frequency domain reference signal can obtain the CIR using the sent reference symbol.
- the signal Z k from a sending end is given as a pseudo noise (PN) sequence so that it has no correlation with k
- the result of Equation (2) is a maximum peak value if a frequency error is zero and a sequence of small values which correspond to noise if a frequency error is not zero.
- PN pseudo noise
- a maximum value detector 124 detects a maximum peak value by applying Equation (2) after cyclically rotating the reception signal X k by ⁇ f i , and the counter 125 finds a rotation amount ⁇ f i where the maximum peak value occurs.
- the rotation amount ⁇ f i is an error F o that is an integer multiple of a frequency error to be detected.
- Equation (3) The relationship is defined by Equation (3):
- F o max ⁇ ⁇ ⁇ f i ⁇ ⁇ max ⁇ ⁇ amp ⁇ [ IFFT ⁇ ⁇ X R ⁇ Z ⁇ ] ⁇ ( 3 )
- Z denotes a phase reference symbol
- X R denotes a reception symbol made up of terms of X ((k+ ⁇ fi))N obtained by cyclically rotating an individual value X k of a reception symbol X in the frequency domain by ⁇ f i .
- a coarse frequency synchronization method according to the conventional OFDM receiver system discussed above makes it possible to actually or theoretically estimate a frequency error in any situation regardless of channel environment and frame synchronization error.
- this method requires a considerable amount of computation. Specifically, this method requires a very complicated IFFT module in order to accurately estimate a frequency error, and causes an excessive time delay due to a long response time.
- the present invention provides a coarse frequency synchronization apparatus in an orthogonal frequency division multiplexing (OFDM) receiver capable of performing stable frequency synchronization with a small amount of computation.
- OFDM orthogonal frequency division multiplexing
- the present invention also provides a coarse frequency synchronization method implemented in the coarse frequency synchronization apparatus.
- the present invention also provides an orthogonal frequency division multiplexing receiver that can perform stable synchronization with a small amount of computation.
- a coarse frequency synchronization apparatus in a frequency synchronizer of an orthogonal frequency division multiplexing (OFDM) receiver.
- the coarse frequency synchronization apparatus includes: a buffer operable to receive a demodulated symbol and output a shifted symbol generated by cyclically shifting the demodulated symbol by a predetermined shift amount; a controller operable to determine a length of summation interval according to a phase coherence bandwidth and a number of sub-bands into which the summation interval is divided, and generate and adjust a symbol time offset according to the number of sub-bands; a reference symbol predistortion portion operable to generate a reference symbol whose phase is distorted by the symbol time offset; a counter operable to determine the shift amount; a partial correlation portion operable to receive the shifted symbol and the reference symbol and calculate a partial correlation value for each of the sub-bands; and a maximum value detector operable to calculate the shift amount where the sum of the partial correlation values is a maximum and output
- a coarse frequency synchronization method for use in an OFDM receiver for performing OFDM demodulation and frequency synchronization.
- the method includes the steps of: (a) receiving a demodulated symbol and outputting a shifted symbol generated by cyclically shifting the symbol by a predetermined shift amount; (b) determining the length of a summation interval according to a phase coherence bandwidth and a number of sub-bands into which the summation interval is divided, and generating a predetermined symbol time offset according to the number of sub-bands; (c) generating a reference symbol whose phase is distorted by the symbol time offset; (d) counting the shift amount; (e) calculating a partial correlation value between the shifted symbol and the reference symbol for each of the sub-bands; and (f) determining the shift amount d where the partial correlation value is a maximum and outputting the shift amount d as an estimated coarse frequency offset value.
- an OFDM receiver including a coarse frequency synchronization apparatus.
- the coarse frequency synchronization apparatus is comprised of: a buffer that receives a demodulated symbol and outputs a shifted symbol generated by cyclically shifting the symbol by a predetermined shift amount; a controller than determines the length of a summation interval according to a phase coherence bandwidth and a number of sub-bands into which the summation interval is divided, and generates and adjusts a symbol time offset according to the number of sub-bands; a reference symbol predistortion portion that generates a reference symbol whose phase is distorted by the symbol time offset; a counter that counts the shift amount; a partial correlation portion that receives the shifted symbol and the reference symbol and calculates a partial correlation value for each of the sub-bands; and a maximum value detector that calculates the shift amount d where the partial correlation value is a maximum and outputs the shift amount d as an estimated coarse frequency offset value.
- FIG. 1 shows an example of the structure of a conventional orthogonal frequency division multiplexing (OFDM) receiver
- FIG. 2 is a graph illustrating the relationship between phase coherence bandwidth and time offset between an original signal and a delayed signal having a frame synchronization error with respect to the original signal, in order to explain a coarse frequency synchronization apparatus and method according to the present invention
- FIG. 3A is a block diagram showing the structure of an OFDM receiver having a coarse frequency synchronization apparatus according to an embodiment of the present invention
- FIG. 3B is a detailed block diagram showing the structure of a reference symbol predistortion portion shown in FIG. 3A ;
- FIG. 4 is a flowchart illustrating a coarse frequency synchronization method according to an embodiment of the present invention
- FIG. 5 schematically shows a process of calculating the correlation between a received reference symbol and a predistorted reference symbol according to the present invention
- FIG. 6 explains the effect of symbol distortion with respect to a time frequency error
- FIGS. 7A and 7B show correlation between a reference symbol and a reception symbol with respect to changes in a symbol time offset
- FIGS. 8A and 8B show results of a simulation of a coarse frequency offset value detection method of the present invention
- FIGS. 9A and 9B show results of a simulation of a conventional coarse frequency offset value detection method.
- FIGS. 10A-10D are graphs showing both theoretical and simulated percentage probabilities of accurately detecting a frequency offset value using a coarse frequency synchronization method according to the present invention versus frame synchronization error.
- f k +f Off denote a subcarrier frequency and a frequency offset, respectively.
- a frequency offset value is measured in units of a multiple of spacing of subcarrier frequency. In general, integer and decimal multiples of subcarrier spacing are separately processed.
- each term of f k +f off is defined as follows:
- Equation (5) a reception signal of an n-th symbol is defined by Equation (5).
- noise has been neglected for convenience in expanding the equation.
- C n,k denotes the k-th transmission signal of the n-th symbol in the frequency domain and N denotes the number of subcarriers.
- Equation (6) a demodulated signal ⁇ ′ n,p in is given by Equation (6):
- the demodulated signal ⁇ ′ n,p is obtained from the reception signal as follows:
- Equation (7) includes a Discrete Fourier Transform (DFT) process, the shift in this equation is a cyclic shift.
- DFT Discrete Fourier Transform
- a correlation value is calculated by sequentially rotating the already known phase reference symbol and reception signal by symbol intervals, and the amount of rotation where the maximum correlation value occurs is determined as an integer multiple of frequency error. This relationship is defined by Equation (8):
- channel coherence bandwidth refers to a statistically measured frequency band where a channel can be deemed as ‘flat’ or passes two signals so that they have approximately the same gain and linear phase over all spectrum components. That is, a channel coherence band is a frequency band in which two different frequency components have a strong correlation. In this case, assuming that the coherence band of a channel is B c , two sine waves having frequency spacing larger than that of coherence band B c are affected within the channel in different ways. Thus, the correlation between the two reception signals cannot be ensured.
- a phase coherence bandwidth is defined as a frequency interval where two signals having a delay in the time domain and generated by performing a DCT on the same signal maintain their correlation in the frequency domain. Analogous to the channel coherence band, it can also mean a frequency band in which the two signals have a strong correlation.
- Equation (9) a time domain signal in the OFDM system be z(t), a delayed signal having a frequency error of T off with respect to z(t) be z(t+T off ), and a frequency domain signal that has undergone a DCT be Z(k), a signal generated by performing a DFT on z(t+T off ) is given by Equation (9):
- N denotes the number of subcarriers.
- the phase coherence bandwidth is defined as a frequency band in which two signals always have a strong correlation. That is, if a frequency band B has the largest bandwidth where a correlation value of the two signals Z(k) and e j2 ⁇ kT off
- 1, the left side of Equation (10) can be expanded as shown in Equation (11):
- Equation (11) the lower bound m of the summations is not fixed, the relation between the frame synchronization error T off and a summation interval K is not clear.
- Equation (12) Equation (12), in which the summations have a lower bound of zero.
- Equation (12) can be combined with Equation (10) to yield Equation (13) which can be used to obtain a phase coherence bandwidth with respect to changes in a frame synchronization error:
- Equation (13) The left side of Equation (13) is a correlation function of two signals z(t) and Z(t+T off ) in the frequency domain with respect to the summation interval K where Z(t+T off ) is a delayed signal having a frequency error of T off . That is, the phase coherence bandwidth refers to a frequency band B where the correlation function of the two signals having the frame synchronization error T off expressed in Equation (13) is always greater than or equal to the threshold T C .
- FIG. 2 is a graph showing computer simulation results of the relation in Equation (13).
- the graph illustrates the relationship between phase coherence bandwidth and time offset between an original signal and a signal having a frame synchronization error with respect to the original signal.
- a bandwidth is represented by a multiple of subcarrier spacing, and the entire frequency band of a channel is set to 1024.
- coherence bandwidth thresholds are set to 0.2, 0.5, 0.9, and 0.99, respectively, the corresponding bandwidths are calculated for a signal time offset that ranges from zero to 100.0 samples.
- phase coherence bandwidth threshold increases, phase coherence bandwidth decreases.
- FIG. 2 shows the relationship between coherence bandwidth and a time offset T off that is the time delay factor.
- the relationship is represented by BW
- bandwidth changes with respect to a time offset in a manner similar to when the coherence bandwidth threshold T C is 0.5.
- the phase coherence bandwidth in the present invention is approximated as
- z(t) and x(t) are a reference signal and a reception signal generated by performing IFFT on the phase reference signal Z(k) and signal X(k) in Equation (8), respectively. It is further assumed that the reception signal x(t) has a time delay, i.e., frame synchronization error. Given these assumptions, there is a reciprocal relation between a frame synchronization error ⁇ t and phase coherence bandwidth on the frequency axis. This relationship means that as the frame synchronization error ⁇ t increases, phase coherence bandwidth on the frequency axis decreases.
- the coarse frequency synchronization method of the present invention is based on coarse frequency synchronization using a correlation value between reference signals.
- a summation interval BWLen is set to be smaller than a phase coherence bandwidth calculated for a reference symbol and a reception symbol having a time offset. That is, in order to calculate a correlation value between a shifted reception symbol and a reference symbol, the summation interval is divided into a plurality of intervals that are smaller than a phase correlation bandwidth of two signals, partial correlation values are calculated for each small interval resulting from the division, and an average or sum of the partial correlation values is taken to determine a shift amount where the maximum correlation value is generated.
- the present invention generates a predistorted phase reference.
- the effect of symbol distortion with respect to a time offset will now be described with reference to FIG. 6 .
- a time offset in OFDM causes phase rotation in proportion to the order of a subcarrier in a sequence of subcarriers.
- a transmission channel is an Additive White Gaussian Noise (AWGN) channel, and accurate frequency synchronization in a reception signal is achieved.
- AWGN Additive White Gaussian Noise
- Equation (14) can be rewritten as Equation (15):
- T s is an OFDM symbol period
- m is the sampling order
- ⁇ is a sampling error that is a time offset.
- a demodulated signal ⁇ ′ n,p obtained from the reception signal is thus expressed by Equation (17):
- P n (p) in Equation (17) that is a value generated by converting noise n(m) to a frequency domain is AWGN having the same variance as the noise n(m) that is also AWGN.
- the effect of noise is not directly related to time synchronization of an OFDM signal.
- Equation (21) the reception signal ⁇ ′ n,p is demodulated by rotating the phase of a transmission signal C n,p to be demodulated.
- the amount of phase rotation is determined as a value proportional to the product of a time offset ⁇ and the position p of a subchannel.
- the reception signal in Equation (21) suffers phase rotation due to a time offset.
- the phase is rotated by ⁇ *p in proportion to the order p of subcarriers.
- the present invention generates a reference symbol whose phase has been predistorted and uses the reference symbol in detecting coarse frequency synchronization, thus allowing more accurate frequency synchronization detection.
- ⁇ corresponds to a symbol time offset ⁇ t i that will be described later.
- FIG. 3A is a block diagram showing an example of the structure of an OFDM receiver having the coarse frequency synchronization apparatus according to an embodiment of the invention.
- the OFDM receiver shown in FIG. 3A is comprised of an OFDM demodulator 30 and a frequency synchronizer 32 .
- the OFDM demodulator 30 consists of an RF receiver 301 , an analog-to-digital converter 302 , an I/Q filter 303 , a frequency corrector 304 , an FFT unit 305 , and a Viterbi decoder 306 .
- the frequency synchronizer 32 consists of a register 321 , a partial correlation portion 322 , a maximum value detector 323 , a counter 324 , a reference symbol predistortion portion 325 , and a controller 326 .
- FIG. 4 is a flowchart illustrating the coarse frequency synchronization method in the OFDM receiver.
- step S 410 a reception symbol X(k) received from the OFDM demodulator is input to the register 321 , and the register 321 cyclically shifts the reception symbol X(k) by a predetermined shift amount d and outputs the shifted symbol X(k+d) to the partial correlation portion 322 .
- step S 420 the controller 326 calculates the length of a summation interval for the phase coherence bandwidth, determines the number K of sub-bands into which the summation interval is divided, generates a predetermined symbol time offset according to the number of sub-bands, and outputs the symbol time offset to the reference symbol predistortion portion 325 .
- step S 430 the reference symbol predistortion portion 325 generates a reference symbol Z(k) whose phase is distorted by the input symbol time offset and outputs the reference symbol Z(k) to the partial correlation portion 322 .
- the configuration and operation of the reference symbol predistortion portion 325 will be described later with reference to FIG. 3B .
- step S 440 assuming that N is the number of subcarriers and the predetermined shift amount d of the shifted signal received by the partial correlation portion 322 is
- the partial correlation portion 322 calculates a partial correlation value between the shifted reception symbol X(k+d), generated by the register 321 shifting X(k) by the predetermined shift amount d, and the predistorted reference symbol Z(k), received from the reference symbol predistortion portion 325 , while counting the shift amount d for each of the K sub-bands, or calculating the sum
- step S 450 the maximum value detector 323 then determines a shift amount d where the sum received from the partial correlation portion 322 has a maximum value, and outputs the determined shift amount d as an estimated coarse frequency offset value.
- an algorithm for calculating Equation (22) is repeated a number of times predetermined by the controller 326 to calculate a coarse frequency offset value.
- N is the number of subcarriers
- K is the number of sub-intervals into which the interval of summation with respect to a correlation function is divided
- N/K is a sub-interval BWLen (See FIG. 5 ) of the summation.
- the reference symbol predistortion portion 325 includes a reference symbol generator 3251 that generates the same reference symbol as a reference symbol sent from a transmitter, a phase rotation portion 3253 that shifts the phase of a phase reference symbol by the symbol time offset received from the controller 326 and generates a phase-distorted reference symbol, and a sin/cos table 3255 that outputs sin and cos values, calculated according to phase values used for phase rotation, to the phase rotation portion 3253 .
- the controller 326 determines sub-intervals BWLen of summation based on the phase coherence bandwidth, divides the entire interval of summation into sub-intervals, and determines the number of sub-bands.
- the controller 326 further calculates a symbol time offset that can be tolerated according to the number of sub-bands, and determines ⁇ t i using the calculated symbol time offset.
- (+) and ( ⁇ ) time offsets may occur so that the time offset is actually generated as ⁇ t i .
- the controller 326 then outputs the generated time offset ⁇ t i to the phase rotation portion 3253 .
- the phase rotation portion 3253 generates a phase-distorted reference signal using the above equation
- the reference symbol is generated according to the order of subcarriers, and the phase rotation portion 3253 generates a complex number e j ⁇ 2 ⁇ p ⁇ ti/T s corresponding to the position of each subcarrier, by which the phase is rotated.
- e j ⁇ 2 ⁇ p ⁇ ti/T s is multiplied by the reference symbol to generate a predistorted phase reference symbol. Since the complex number e j ⁇ 2 ⁇ p ⁇ ti/T s is not suitable for use in an actual embodiment, complex number multiplication is performed after representing it in the form of cos ⁇ +j sin ⁇ . In this case, values of cos ⁇ and sin ⁇ are obtained by referring to the sin/cos table 3255 .
- FIGS. 7A and 7B show correlation between the reference signal and the reception signal with respect to change in symbol time offset. It is evident from these figures that coherence bandwidth varies with symbol time offset. Thus, by performing a coarse frequency synchronization algorithm after setting an appropriate coherence bandwidth, a coarse frequency offset can be effectively estimated.
- FIGS. 8A and 8B are graphs illustrating the results of this simulation.
- FIGS. 9A and 9B show the results of a simulation performed according to a conventional coarse frequency offset value detection method.
- the simulations were performed under the conditions that signal-to-noise (SNR) ratio is 5 dB in a Gaussian channel, the number of subcarriers is 1024 , and a frequency error is ⁇ 62.4 times the number of subcarriers.
- SNR signal-to-noise
- the simulation results shown in FIGS. 8A and 9A are for a symbol time offset of 0.0, and the simulation results shown in FIGS. 8B and 9B are for a symbol time offset of 10.0.
- a correlation function over the entire band in a Gaussian channel was applied.
- the entire channel bandwidth was divided into 32 subbands, and the sum of correlation values for each subband was calculated.
- frequency is plotted on the horizontal axis and correlation value is plotted on the vertical axis.
- the given frequency offset value is ⁇ 62.4, if a maximum peak value is generated at a value of ⁇ 62 on the horizontal axis, it means that a coarse frequency offset value is accurately detected.
- the results of the simulation performed according to the coarse frequency synchronization method of the present invention show that a maximum value occurs at the value of ⁇ 62 on the horizontal axis, corresponding to the given frequency offset value in the case of no time offset as shown in FIG. 8A as well as in the case of a time offset of 10.0 as shown in FIG. 8B . This shows that the coarse frequency offset value is accurately detected in the present invention.
- the coarse frequency offset value is accurately detected in the case of no symbol time offset as shown in FIG. 9A .
- a symbol time offset of 10.0 as shown in FIG. 9B , no peak appears at the value of ⁇ 62 on the horizontal axis corresponding to the given frequency offset value, showing that the coarse frequency offset value was not accurately detected.
- FIGS. 10A-10D are graphs illustrating percentage probability of accurately detecting a course frequency offset value versus frame synchronization error value.
- the purpose of these graphs is to explain accuracy in error detection using the coarse frequency synchronization method of the present invention.
- both theoretical data and data obtained by simulation are plotted.
- the simulation conditions are that the channel is a Gaussian channel with an SNR ratio of 5 dB and a sample time offset interval is in the range of ⁇ 50-+50.
- the frequency offset is a value in the range of ⁇ 510 to +510.
- FIGS. 10A-10D show for comparison theoretical intervals and intervals obtained by simulations where a frequency offset value can be accurately detected according to the coarse frequency synchronization method of the present invention.
- the theoretical intervals are represented by a thick solid line and the intervals obtained by simulation are represented by a thin solid line.
- the number of subcarriers is 1024 and 2048 , respectively, and the length of a guard interval is 128 samples.
- the simulations were performed to calculate the probability of accurately detecting a frequency offset value by applying a frequency offset to a particular time offset value 100 times for each repetition.
- results o f the simulations performed to evaluate the performance of the present invention show that calculating a correlation value by dividing the summation interval into sub-bands according to the present invention can accurately detect a coarse frequency offset value with respect to a time offset value that can be tolerated in frame synchronization, in contrast to the case of not dividing the summation interval.
- the amount of computation is proportional to N 2 based on the amount of computation required for complex multiplication in an OFDM system using N subcarriers.
- the conventional method using channel response requires the amount of computation to be proportional to
- N 2 2 ⁇ log 2 ⁇ N within the tolerance given by a coarse frame synchronization algorithm while maintaining stable operation.
- the exact amount by which computation is reduced varies depending on the number of subcarriers. Specifically, the amount by which computation is reduced is the same as the amount of computation required to perform N IFFT operations where N is the number of subcarriers. For example, if the number of subcarriers is 1024, the present invention performs only 1 ⁇ 6 of the amount of computation conventionally performed, and if the number of subcarriers is 2048, the present invention performs only 1/11 of the amount of computation conventionally performed.
- the coarse frequency synchronization method and apparatus can prevent degradation in performance when a symbol timing error is greater than or equal to ⁇ 1( ⁇ 1 ⁇ 2) by dividing the summation interval for calculating a correlation value between the received symbol and reference symbol into a predetermined number of sub-intervals determined according to a local coherence bandwidth.
- this invention can accurately achieve coarse frequency synchronization even when a symbol timing error is greater than ⁇ 5 samples under poor channel conditions, by predistorting the reference symbol used in calculating a correlation value with the received symbol.
Abstract
Description
where Z denotes a phase reference symbol and XR denotes a reception symbol made up of terms of X((k+Δfi))N obtained by cyclically rotating an individual value Xk of a reception symbol X in the frequency domain by Δfi.
where Δf denotes a number that represents the frequency offset of subcarrier by a multiple of subcarrier spacing and can also be replaced by the sum of an integer Δfi and a decimal Δff that satisfies the condition −½<Δff<½. Given this condition, a reception signal of an n-th symbol is defined by Equation (5). Here, noise has been neglected for convenience in expanding the equation.
where Cn,k denotes the k-th transmission signal of the n-th symbol in the frequency domain and N denotes the number of subcarriers.
where ((k+d))N is a sign representing a modulo-N summation operation, X(k) is the k-th reception signal after performing a DFT, and Z(k) is the k-th phase reference signal. Also, X(k) and Z(k) are frequency domain signals. However, this method can correct a frequency error when frame synchronization occurs but it cannot when frame synchronization does not occur. This problem can be solved by analyzing a phase coherence bandwidth for the reception signal and phase reference signal.
where TC denotes a threshold and N denotes the number of subcarriers. If an OFDM signal satisfies |Z(k)|=1, the left side of Equation (10) can be expanded as shown in Equation (11):
where N is the number of subchannels, Cn,k is a signal in the n-th symbol transmitted through the k-th subchannel, Ψ′n,k is the k-th subcarrier signal, and n(t) is AWGN with variance σn 2. Equation (14) can be rewritten as Equation (15):
where fk is a subcarrier frequency and equal to fk=k/Ts.
In this case, Ts is an OFDM symbol period, m is the sampling order, and τ is a sampling error that is a time offset.
is expressed by Equation (18):
a=e j2π(k−p)N (19)
the
of partial correlation values.
where N is the number of subcarriers, K is the number of sub-intervals into which the interval of summation with respect to a correlation function is divided, and N/K is a sub-interval BWLen (See
Thus, the method of the present invention can reduce the additional amount of computation
within the tolerance given by a coarse frame synchronization algorithm while maintaining stable operation. The exact amount by which computation is reduced varies depending on the number of subcarriers. Specifically, the amount by which computation is reduced is the same as the amount of computation required to perform N IFFT operations where N is the number of subcarriers. For example, if the number of subcarriers is 1024, the present invention performs only ⅙ of the amount of computation conventionally performed, and if the number of subcarriers is 2048, the present invention performs only 1/11 of the amount of computation conventionally performed.
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JP2004282759A (en) | 2004-10-07 |
EP1460814A2 (en) | 2004-09-22 |
US20040179625A1 (en) | 2004-09-16 |
DE602004018052D1 (en) | 2009-01-15 |
EP1460814A3 (en) | 2006-12-13 |
KR20040081664A (en) | 2004-09-22 |
CN1531214A (en) | 2004-09-22 |
JP4263119B2 (en) | 2009-05-13 |
KR100528332B1 (en) | 2006-01-09 |
EP1460814B1 (en) | 2008-12-03 |
CN100463371C (en) | 2009-02-18 |
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